本文在实Hilbert空间中提出了一种求解拟单调变分不等式问题的新的自适应向前向后算法,并在合理的假设下证明了由算法产生的迭代序列强收敛到变分不等式解集的一个元素。最后数值实验阐明了算法的有效性与优越性。
In this paper, we propose a new adaptive forward-backward algorithm to solve the quasimonotone variational inequality problem in real Hilbert spaces. Under reasonable assumptions, we prove that the iterative sequence generated by the algorithm converges strongly to an element of the solution set of the variational inequality problem. Finally, numerical experiments show the effectiveness and superiority of the new algorithm.
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